Mixers multiply signals in the time domain. Because time domain multiplication corresponds to convolution in the frequency domain, mixing two sinusoids produces output sinusoids at the sum and difference of the respective frequencies of the input sinusoids. Mixers thus find widespread use in communication signal transmitters and receivers, where they are used to shift signals from one frequency range to another. For example, mixers downconvert received signals from the carrier frequency used in transmission to intermediate and/or baseband frequencies suitable for processing. Conversely, on the transmit side, mixers upconvert baseband signals to carrier frequencies used in signal transmission.
In a simple example, an input signal is shifted to a desired output frequency by mixing it with a local oscillator or “LO” signal. The LO signal has an LO frequency chosen so that the sum or difference of the LO frequency and the input signal frequency corresponds to the desired output frequency, and output filtering eliminates the unwanted sum or difference frequency. As with many aspects of signal processing, practical implementations of mixers result in the generation of output signal components at undesired frequencies.
For example, the input signal frequency and/or the LO frequency may bleed through the mixer, although single-balanced and double-balanced configurations may be used to eliminate or greatly reduce these problems. A greater challenge arises in the generation of unwanted harmonics associated with the use of “switched” mixers, wherein the local oscillator waveform is a squarewave or other stepped waveform, rather than an analog sinusoid. The use of switched circuitry for mixing allows for greater digitization of the mixing circuitry and its corresponding control, but results in more harmonic content at the mixer output unless mitigations are adopted.
Harmonic rejection mixers adopt various approaches to reducing the harmonic content of their output signals. One type of harmonic rejection mixer having particularly advantageous characteristics operates as a time-discrete and time-variant transconductance. Rather than using an explicit LO waveform to mix with an input signal, this type of mixer applies the input signal to a variable conductance circuit and switches that circuit through a sinusoidal sequence of conductance values at a frequency corresponding to the desired LO frequency. For reasons of spectral purity and low complexity, this particular type of harmonic rejection mixer operates with an integer number of samples per LO period. The number of samples used to represent one period of the LO waveform is referred to as the oversampling rate or OSR.
The harmonic rejection performance of such mixers depends on a complex set of variables, but ultimately can be understood as depending on the fidelity or accuracy at which the variable conductance can be controlled to behave as a sinusoidally varying conductance. In turn, the accuracy of control depends on the resolution of control for the variable conductance. More plainly, each sample value in the sequence should map to a conductance value corresponding to a discrete sample point on the ideal LO waveform.
Different OSRs yield different harmonic rejection performance for given input and output frequencies of interest. Because communication devices are increasingly required to operate in multiple carrier frequency bands, and because the simultaneous use of two or more carrier frequencies—“carrier aggregation”—is an increasingly exploited technology in current and developing wireless standards, the particular OSR that a harmonic rejection mixer should operate with will change in dependence on the particular frequencies of interest at any given time.
In a general approach, the harmonic rejection mixer will use a preprogrammed sequence of sample values representing the LO waveform. In a quadrature configuration, two such mixers will operate ninety degrees out of phase with respect to each other. Quadrature mixing is used to process in-phase and quadrature components of communication signals. Such operation applies to mixer operation in a variety of contexts, including image rejection and various up- and down-conversion applications, with the common characteristic being operation on a clocked basis, using discrete sequences of sample values.
Achieving quadrature operation is straightforward when the OSR of such sequences is divisible by four, because the required ninety-degree phase shift between the in-phase and quadrature mixer elements corresponds to an integer number of sequence positions in the LO waveform sequence. Thus, the same sequence can be used by the in-phase and quadrature mixer elements, with the quadrature mixer element simply offsetting the sequence by the number of sequence positions corresponding to the desired quadrature shift.
Such operation is not possible when the OSR does not divide by four, and the quadrature phase shift requires the use of a different sequence of sample values. That is, one known approach to handling a range of OSRs, including OSRs not divisible by four, involves applying different sequences to the in-phase and quadrature mixer elements. The sequence applied to the quadrature mixing element comprises sample values that are computed to reflect a ninety degree phase shift relative to the sample values of the sequence applied to the in-phase mixer element.
This approach thus requires having two sets of sequences, including a pair of in-phase and quadrature sequences for each OSR of interest. Moreover, although each sequence may represent LO waveforms with low harmonic content, the magnitude and phase of the fundamental LO tones generally become different. This translates to a severely limited image rejection ratio for the overall mixer, because of unavoidable non-linearity associated with quantized control of the variable conductance. In other words, using different sample values between the two mixers effectively means that the LO waveform used by the quadrature mixer element is not identical to the LO waveform used by the in-phase mixer element.